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If the radii of nuclei of ²⁷₁₃Al and ⁶⁴₃₀Zn are R₁ and R₂ respectively, then (R₁)/(R₂)= ______.

Asked in GUJCET 2009 · Nuclear radius and density

• (1) (64)/(27)
• (2) 3/4
• (3) (27)/(64)
• (4) 4/3

Step-by-step solution

Why the other options are wrong

• (1) (64)/(27) is the ratio of the mass numbers the wrong way up and with the cube root left out; the radius goes as A^1/3.
• (3) (27)/(64) is (A₁)/(A₂) with the cube root left out. Taking the cube root of both numbers gives 3/4.
• (4) 4/3 is (R₂)/(R₁) — zinc over aluminium, the inverse of what is asked; aluminium is the smaller nucleus, so (R₁)/(R₂) must be less than 1.

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